Puzzle 1: How many times do the hands of a clock coincide in a day?
A.) 20 B.) 21
C.) 22 D.) 24
Answer: Option ‘C’
Explanation: The hands of a clock coincide 11 times in every 12 hours
(Since between 11 and 1, they coincide only once, i.e. at 12 o’clock).
==> The hands coincide 22 times in a day.
Puzzle 2: How many times are the hands of a clock at right angles in a day?
A.) 22 B.) 44
C.) 38 D.) 48
Answer: Option ‘B’
Explanation: In 12 hours, they are at right angles 22 times.
==> In 24 hours, they are at right angles 44 times.
Puzzle 3: How much does a watch lose per day, if its hands coincide every 64 minutes?
A.) 32 8/11min B.) 36 5/11min
C.) 90min D.) 96min
Answer: Option ‘A’
Explanation: 55 min. spaces are covered in 60 min.
60 min spaces are covered in (60/55 * 60) min = 65 5/11 min
Loss in 64 min = (65 5/11- 64) = 16/11 min
Loss in 24 hrs = (16/11 * 1/64 * 24 * 60) min
= 32 8/11 min
Puzzle 4: How many times in a day the hands of a clock are straight?
A.) 22 B.) 21
C.) 43 D.) 44
Answer: Option ‘D’
Explanation: In 12 hours, the hands coincide or are in opposite direction 22 times.
In 24 hours, they are at right angles 22 times.
Puzzle 5: At what time between 4 & 5 will the hands of a watch point in opposite directions?
A.) 43 min past 4 B.) 42 5/11 min past 4
C.) 50 4/11 min past 4 D.) 40 min past 4
Answer: Option ‘C’
Explanation: At 4 o’clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30min. spaces apart.
Minute hand will have to gain 5 min. spaces.
55min spaces are gained in 60 min.
5 min. spaces are gained in (60/55 * 50) min. or 54 6/11 min.
Required time = 54 6/11 min. past 4.